If3,x,y,18 are in arithmetric progression , find the value of x and y
you know you have a common difference.
18-3 = 15
15/3 = 5
add that to get each next term.
IF AN A P = 3, X Y,18,FIND THE UNMERICAL VALUES OF X AN Y
Correct
To find the value of x and y in an arithmetic progression (AP), we need to use the formula for the nth term of an AP:
an = a1 + (n-1)d
Here, a1 is the first term of the AP, d is the common difference, and an is the nth term.
In this case, we are given the values a1 = 3, an = 18, and we need to find the values of x and y.
Since we don't know the position of x and y in the AP, let's assume that x is the second term (a2) and y is the third term (a3).
So, we can set up the following equations:
a1 + (2-1)d = x (Equation 1)
a1 + (3-1)d = y (Equation 2)
Since a1 = 3:
3 + d = x (Equation 1)
3 + 2d = y (Equation 2)
Now, we also know that an = 18:
a1 + (n-1)d = 18
3 + (4-1)d = 18
3 + 3d = 18
Solving this equation, we find that d = 5.
Substituting the value of d back into Equation 1:
3 + 5 = x
x = 8
Similarly, substituting the value of d back into Equation 2:
3 + 2(5) = y
3 + 10 = y
y = 13
Therefore, the value of x is 8 and the value of y is 13 in the given arithmetic progression.